Integer Factorization: What’s Up Lately (2 April 2023)


What’s got me all excited lately mathematically has been further exploration of the odd positive integers and the way their remainder series behave when translated into Remainder Lines on the Zone Grid. I established the construction of such a grid and the lines in question in a post a few weeks ago, and now I’m posting to give you an update. I’ve not found anything yet that gives me further insight into speedy methods of factorization, but these concepts are young, and there is plenty of numerical behavior still for me to explore.

Here is a picture of what I’ve been trying to graph today. Just keeping folks up to date. One clarification of the comments on the image is that it is possible – frequent, even – that the Remainder Lines intersect the Zone Lines at non-integer points. They will still be rational, but they will not correspond to factorization solutions. Also, isn’t the distribution of just these few odd integers so far, in terms of their remainder series’ starting points, such a fascinating mixture of order and (apparent) chaos?


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